The specific description of the Create Water spell on page 215 of the Player's Handbook says:
Water can be created in an area as small as will actually contain the liquid, or in an area three times as large
Note: Conjuration spells can't create substances or objects within a creature.
Thus you couldn't create the water directly inside the creature, both because it is a creature, and because it's mouth would (most probably) be too small to contain the entire volume created.
This does not stop you from conjuring the water in an appropriately inanimate container and then forcing it into the creature.
No to the first, can't create it within the creature. As to the second, if you could drown a creature by creating sufficient water around them... that depends on where we are and how much water*.
If standing in relatively flat land, creating the water over the head would just lead to the equivalent to the "Ice Bucket Challenge" or the ritual pouring of water over a coach's head at the end of a sports game. You could argue for some surprise value, but gravity keeps it from staying at nose level for too long.
At 8 gallons per cubic foot, you'd need to be around 144th level to cover someone in a sarcophagus with a foot of water. But what about their head? At 4th level you could cover someone's head reliably enough. They'd have to be unable to remove their head from said water. This wouldn't be terribly doable in combat, and if the goal is SOLELY to kill, it's not terribly effective.
However, as an execution ritual it works fine. It also works well for a magical murderer. Add in a custom spell (or side-effect of another spell) to freeze water, and you've got yourself a D&D take on the old "ice bullet" mystery!
* = And, of course, depends on your GM. If your GM says that your Half-Orc who's wrestled a kobold can put his hand over the kobold's mouth and use Create Water to suffocate/aid in suffocating the critter, that makes sense... but it also makes sense if your GM says "No, that's not the point of the spell so it just doesn't work that way."